# Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.

Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.

1. Pyramid four sides In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
2. The tent The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
3. Wall height Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
4. Axial cut The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
5. Pyramid 4sides Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
6. Support colum Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.
7. Rotating cone Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
8. Cube diagonals Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
9. Roof 8 How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
10. Pyramid The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
11. Cone The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
12. Hexagonal pyramid Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
13. Regular triangular prism Calculate the surface area of body of regular triangular prism, when the length of its base edge is 6.5 cm and height 0.2 m.
14. Above Earth To what height must a boy be raised above the earth in order to see one-fifth of its surface.
15. Airplane Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
16. The cylinder base The cylinder with a base of 8 dm2 has a volume of 120 liters. From a cylinder fully filled with water, 40 liters of water was removed. At what height from the bottom /with precision to dm/ is the water level?
17. Prism Calculate the surface area and volume of a prism with a body height h = 10 cm and its base has shape of a rhomboid with sides a = 5.8 cm, b = 3 cm and the distance of its two longer sides is w = 2.4 cm.
18. Cube Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.
19. Cuboid - volume, diagonals The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?
20. Roof of the church The cone roof of the church has a diameter of 3m and a height of 4m. What is the size of the side edge of the church roof (s) and how much sheet will be needed to cover the church roof?

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